# How and where does air that is displaced by a constant moving vehicle flow?

How does air that is displaced by a constant moving car move?

When a car is driving with constant speed, there is air displaced in front of the car. Let's say the surface of the car view flat from front is 2m² and the vehicle is moving at 40m/s, that is 80m³/s. What I am trying to figure out is approximately where and how fast this air moves around the car.

Now I have trouble comparing a moving car to a wind tunnel, actually I can't understand why it would behave the same. What is giving me a headache:

First what I currently imagine from pictures or videos of cars in a wind tunnel: Air is blown with constant speed at a car. The area of the airflow is larger than the car. Then the wind lines compress around the roof of the car, meaning the wind has to go faster. Also the lines move up. From wind tunnel videos it can be seen that they compress quite a lot. It looks approximately that if the car height is e.g. 1.5 meters and the air blown has a height of 3 meters than in the end it passes a section with a height of less than 1.5 meters above the car - which would mean more than double of the velocity?

Now if I imagine car moving at same speed along a road, no wind. Relative to an observer the air some space in front of the car has 0 velocity. Now as the car is moving air in front of it has to be displaced (a lot actually). Now my expectation is that the displaced air is being pushed across the car in backward direction of travel, and again the flow is being compressed due to the cars shape, so relative to an oberserver the displaced air moves in reverse direction of the car approximately with the same speed as in the wind tunnel.

But this means, if the car is moving 40m/s from right to left, then the air has to be moving from left to right (with more than 40m/s as the area is also compressed) at least as long as it passes the roof of the car. It can't move forward as it is pushed by the air ahead of the car. Is that correct? This means the relative speed between the air and the car across the roof is more than 80m/s.

Now I have some trouble thinking about this, as I can read in different publications that air close to vehicles is not moving in opposite direction, actually it is being dragged in the direction of the vehicle but with a low speed. I found articles about this: For trains A review of train aerodynamics Part 1 – Fundamentals https://core.ac.uk/download/pdf/185479708.pdf - speed of air relative to the train is positive in the diagrams

Or this: Researchgate Drag explained by Newtonian mechanics https://www.researchgate.net/profile/Nicholas-Landell-Mills/publication/337934778_Why_drag_and_KE_are_proportional_to_velocity2/links/6239df1259c2363ae65f3b04/Why-drag-and-KE-are-proportional-to-velocity2.pdf?origin=publication_detail which depicts 2m/s air speed in direction of travel when the car is moving 33m/s.

Also I saw exercises with a train driving in a confined space (tunnel) where the pressure in he tunnel should be calculated and found contradicting opinions: Some people saying ideally all the displaced air is flowing in reverse direction in the tunnel, other saying the air is pushed ahead in front of the train.

But know that gives me a real headache. If the air is moving in direction of the vehicle (with a low speed, a lot lower than the travel speed) - where does the displaced air then move? Is it just pushed "away" far away of the vehicle and not into the airflow lines closes to the vehicle at all? This seems to be indicated by the measurements. But then I do't understand how there would be a lift and higher air speeds across vehicle tops at all. Or is this about different layers that some of the displaced air is being pushed close over the car (how close) and some of the air pushed far away to the sides (how far)? Is compression involved or can I imagine that air is not compressed? I don't want to calculate the exact numbers, but I want to get a basic understand of the movement, speed and volumes involved.

I also tried to imagine the extremes, a flat surface with maximum drag, and an airfoil with minimum drag, I end up with the same question.

Question summarized: Where and how fast does the displaced air from a constant moving vehicle move?

Help would be gladly appreciated, it seems so basic yet I have trouble imagining it.

• Rest assured that NASA, ESA, etc., and the automotive and aerospace industry have considered this. They employ the best engineers. I suspect they use active walls can absorb pressure changes. You should look for better sources than 'Some people say'. Commented May 8, 2022 at 11:02

Consider a hallway with people walking at constant speed in one direction. Now imagine there is a partial obstruction, so the hallway becomes narrower. People will move faster there, so the same number of people per unit of time can pass the obstruction.

Larger obstructions will cause traffic to slow down, but here we consider a small one which is easily negotiated.

The same happens with air flowing around a car. It speeds up so it needs less cross section for the same mass flow. Once the car becomes supersonic, though, things change because now density will change significantly, too, and the smaller cross section can be achieved by slower, denser flow.

Potential flow theory will tell you how fast the air will flow at each point around the obstacle.

Regarding your measurements: A train does not have the same smooth surface as a plane or a well-designed automobile (hint: Pickups or SUVs don't belong to this class), so it will pull a lot of air with it. What counts here is the combination of train plus surrounding air.

• Thanks for the reply, and I think I get that "forward" direction. Commented May 10, 2022 at 16:46
• Where I still have the confusion: The vehicle moves forwards. So air in front of it is pushed away (and basically "missing" behind the vehicle). Also there is even more air dragged along in the direction of the vehicle (slipstream due to the boundary layer). Where is the return path of the air that was in front of the vehicle? It cant push everything to the front indefinitely. Commented May 10, 2022 at 16:52
• @rubikus There is nothing missing. Air flows around the vehicle and fills in what is left behind by the passing body. The mass of what is dragged along is miniscule. Commented May 10, 2022 at 18:31
• I added a drawing to the post explaing where I have difficulties. I imagine that like you said air is pushed around the vehicle to fill the gap. Which means for an outside observer the air itself also has to move reverse to the vehicle travelling. But if I read publications measuring/modeling the air speed even 3 meters away from the train it actually moves along with the train. One more source I found yesterday: The calculation of train slipstreams using large-eddy simulation researchgate.net/publication/… Commented May 11, 2022 at 7:59